JOURNAL OF GEOPHYSICAL RESEARCH: ATMOSPHERES, VOL. 118, 11,847–11,862, doi:10.1002/jgrd.50874, 2013
Characterizing sampling biases in the trace gas climatologies
of the SPARC Data Initiative
M. Toohey,1 M. I. Hegglin,2 S. Tegtmeier,1 J. Anderson,3 J. A. Añel,4,5 A. Bourassa,6
S. Brohede,7,8 D. Degenstein,6 L. Froidevaux,9 R. Fuller,9 B. Funke,10 J. Gille,11,12
A. Jones,13 Y. Kasai,14 K. Krüger,1,15 E. Kyrölä,16 J. L. Neu,8 A. Rozanov,17 L. Smith,11
J. Urban,7 T. von Clarmann,18 K. A. Walker,13 and R. H. J. Wang 19
Received 31 May 2013; revised 4 September 2013; accepted 28 September 2013; published 21 October 2013.
[1] Monthly zonal mean climatologies of atmospheric measurements from satellite
instruments can have biases due to the nonuniform sampling of the atmosphere by the
instruments. We characterize potential sampling biases in stratospheric trace gas
climatologies of the Stratospheric Processes and Their Role in Climate (SPARC) Data
Initiative using chemical fields from a chemistry climate model simulation and sampling
patterns from 16 satellite-borne instruments. The exercise is performed for the long-lived
stratospheric trace gases O3 and H2O. Monthly sampling biases for O3 exceed 10% for many
instruments in the high-latitude stratosphere and in the upper troposphere/lower
stratosphere, while annual mean sampling biases reach values of up to 20% in the same
regions for some instruments. Sampling biases for H2O are generally smaller than for O3,
although still notable in the upper troposphere/lower stratosphere and Southern Hemisphere
high latitudes. The most important mechanism leading to monthly sampling bias is
nonuniform temporal sampling, i.e., the fact that for many instruments, monthly means are
produced from measurements which span less than the full month in question. Similarly,
annual mean sampling biases are well explained by nonuniformity in the month-to-month
sampling by different instruments. Nonuniform sampling in latitude and longitude are
shown to also lead to nonnegligible sampling biases, which are most relevant for
climatologies which are otherwise free of biases due to nonuniform temporal sampling.
Citation: Toohey, M., et al. (2013), Characterizing sampling biases in the trace gas climatologies of the SPARC Data
Initiative, J. Geophys. Res. Atmos., 118, 11,847–11,862, doi:10.1002/jgrd.50874.
1.
Introduction
[2] Stratospheric trace gas observations are often used
to produce monthly zonal mean data sets, or climatologies
[e.g., von Clarmann et al., 2012; Grooß and Russell, 2005;
Hassler et al., 2009; Jones et al., 2012; Randel and Wu,
2007]. Monthly zonal mean data products are typically used
as prescribed forcing for models [e.g., Cionni et al., 2011]
Additional supporting information may be found in the online version of
this article.
1
GEOMAR Helmholtz Centre for Ocean Research Kiel, Kiel, Germany.
2
Department of Meteorology, University of Reading, Reading, UK.
3
Atmospheric Science, Hampton University, Hampton, Virginia, USA.
4
Smith School of Enterprise and the Environment, University of Oxford,
Oxford, UK.
5
EPhysLab, Universidade de Vigo, Ourense, Spain.
6
Institute of Space and Atmospheric Studies, University of Saskatchewan,
Saskatoon, Saskatchewan, Canada.
7
Department of Earth and Space Sciences, Chalmers University of
Corresponding author: M. Toohey, GEOMAR Helmholtz Centre for
Ocean Research Kiel, Düsternbrooker Weg 20, 24105 Kiel, Germany.
([email protected])
©2013. American Geophysical Union. All Rights Reserved.
2169-897X/13/10.1002/jgrd.50874
and are also useful for comparison with similarly averaged
chemistry climate model output [e.g., Grewe et al., 2012;
SPARC CCMVal, 2010].
[3] Monthly zonal mean data sets can be constructed
through a variety of methods. A simple method involves
binning observations into latitude and month bins and calculating average values for each bin. This is the method used
Technology, Göteborg, Sweden.
8
Now at FluxSense AB, Göteborg, Sweden.
9
Jet Propulsion Laboratory, California Institute of Technology, Pasadena,
California, USA.
10
Instituto de Astrofísica de Andalucía, Granada, Spain.
11
National Center for Atmospheric Research, Boulder, Colorado, USA.
12
Center for Limb Atmospheric Sounding, University of Colorado Boulder,
Boulder, Colorado, USA.
13
Department of Physics, University of Toronto, Toronto, Ontario, Canada.
14
National Institute of Information and Communications Technology,
Koganei, Japan.
15
Now at Department of Geosciences, University of Oslo, Oslo, Norway.
16
Finnish Meteorological Institute, Helsinki, Finland.
17
Institute of Environmental Physics (IUP), University of Bremen, Bremen,
Germany.
18
Karlsruhe Institute of Technology, Institute for Meteorology and
Climate Research, Karlsruhe, Germany.
19
School of Earth and Atmospheric Sciences, Georgia Institute of
Technology, Atlanta, Georgia, USA.
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Table 1. Participating Instruments With the Time Period Used to Define the Sampling Pattern for Each Instrument
Instrument
ACE-FTS
Aura MLS
GOMOS
HALOE
HIRDLS
MIPAS
OSIRIS
POAM II
POAM III
SAGE II
SAGE III
SCIAMACHY
SMILES
SMR
TES
UARS MLS
Full Name
Mission Reference
Sample Reference Period
Atmospheric Chemistry Experiment–Fourier Transform Spectrometer
Aura Microwave Limb Sounder
Global Ozone Monitoring by Occultation of Stars
Halogen Occultation Experiment
High Resolution Dynamics Limb Sounder
Michelson Interferometer for Passive Atmospheric Sounding
Optical Spectrograph and Infrared Imager System
Polar Ozone and Aerosol Measurement II
Polar Ozone and Aerosol Measurement III
Stratospheric Aerosol and Gas Experiment II
Stratospheric Aerosol and Gas Experiment III
Scanning Imaging Absorption Spectrometer for Atmospheric Chartography
Superconducting Submillimeter-Wave Limb Emission Sounder
Submillimetre Radiometer
Tropospheric Emission Spectrometer
UARS Microwave Limb Sounder
Bernath et al. [2005]
Waters et al. [2006]
Bertaux et al. [2010]
Russell et al. [1993]
Gille et al. [2008]
Fischer et al. [2008]
Murtagh et al. [2002]
Glaccum et al. [1996]
Lucke et al. [1999]
McCormick et al. [1989]
Thomason and Taha [2003]
Bovensmann et al. [1999]
Kikuchi et al. [2010]
Murtagh et al. [2002]
Beer [2006]
Waters et al. [1999]
2005
Jan 2005
2003
1994
Sep 2006
Jan 2009a
2009
1995
2001
1990
2003
2010
Oct 2009 – Apr 2010
2010
Jul 2007
1992
a
The MIPAS sampling pattern used here refers to the nominal reduced spectral resolution measurement mode, which was the regular MIPAS measurement
mode from 2005 to 2012.
by the Stratospheric Processes and Their Role in Climate
(SPARC) Data Initiative [Hegglin and Tegtmeier, 2011;
M. I. Hegglin et al., SPARC Data Initiative: Comparison
of trace gas and aerosol climatologies from international
satellite limb sounder, manuscript in preparation, 2013],
which aims to produce such climatologies for a number of
stratospheric trace gas measuring limb sounding instruments
to be used in model-observation comparisons and help guide
future data merging activities.
[4] Each observation-based climatology is an estimate of
the true atmospheric mean state; however, differences between the observation-based climatology and the truth may
arise for a number of reasons. In many cases, the largest
source of error in the climatology is due to errors in the measurements themselves. These errors are present in individual
measured profiles and can be best estimated through careful
comparison of coincident profiles. However, the construction
of climatologies may itself introduce additional errors. The
choice of averaging technique can lead to differences in the
produced climatologies [Funke and von Clarmann, 2012].
The random error in a climatological mean due to the finite
and potentially nonuniform sampling of an atmospheric field
was investigated by Toohey and von Clarmann [2013]. Here
we investigate how such sampling issues may lead to systematic errors, or biases, in atmospheric climatologies.
[5] Sampling bias is an error in a computed quantity which
arises due to unrepresentative sampling of the population. In
the estimation of an atmospheric mean value, sampling bias
may occur when the atmospheric state within the time-space
domain to be averaged over is not uniformly sampled. The
magnitude of sampling bias will also be related to the degree
and structure of the variability: If the atmospheric variability
is weak, then nonuniformity of sampling will not strongly
bias the sample mean compared to the population mean.
Conversely, when variability is strong, then nonuniform sampling may lead to significant sampling bias.
[6] The impact of sampling and averaging on observationbased climatologies of tropospheric fields such as temperature,
clouds, and chemical trace gases has been examined by a number of prior studies [e.g., Aghedo et al., 2011; Engelen et al.,
2000; Guan et al., 2013]. The central technique of these studies
is to subsample climate model or reanalysis fields based on the
sampling patterns of the instruments of interest and then to
quantify differences between the fully resolved raw fields and
the instrument-sampling-pattern-based sampled fields.
[7] In the present study, we use a similar technique as the
above cited works, making use of chemistry climate model
output, and sampling the model fields based on the sampling
patterns of a suite of satellite instruments. However, we focus
on instruments measuring stratospheric trace gas species,
many of which have smaller sample density than the (often
nadir viewing) instruments investigated in previous studies
focusing on tropospheric measurements. Furthermore, we focus on the effect of averaging within 5° latitude bands, which
is a coarser horizontal resolution than that typically used in
prior studies. We use sampling patterns for 16 instruments,
all of which are participants in the SPARC Data Initiative.
We apply the sampling exercise to modeled O3 and H2O
fields and characterize the structure and magnitude of the potential sampling biases associated with the sampling pattern
of each instrument for the two chemical species. The results
of this study should be used to help interpret instrumental
climatology comparisons within the SPARC Data Initiative
for O3 and H2O (Tegtmeier et al. [2013] and Hegglin et al.
[2013], respectively) and inform future use of the climatologies for other purposes such as model comparisons.
2.
Data and Methods
2.1. Instrumental Sampling Patterns
[8] Instruments participating in the SPARC Data Initiative
and which are used in the present study are listed in Table 1,
and include the limb emission sounders Aura MLS, HIRDLS,
MIPAS, SMR, SMILES and UARS MLS, the limb scattering
sounders SCIAMACHY and OSIRIS, the solar occultation instruments ACE-FTS, HALOE, POAM II, POAM III, SAGE
II and SAGE III as well as the stellar occultation instrument
GOMOS. We have also included the nadir-viewing TES emission sounder, which is used in the SPARC Data Initiative evaluation of upper troposphere/lower stratosphere (UTLS) ozone
observations (J. L. Neu et al., The SPARC Data Initiative:
Comparison of upper troposphere/lower stratosphere ozone
climatologies from limb-viewing instruments and the nadirviewing Tropospheric Emission Spectrometer (TES), submitted
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TOOHEY ET AL.: SAMPLING BIASES IN CLIMATOLOGIES
Figure 1. Monthly sample count in 5° latitude bins for 16 instrumental sampling patterns. Gray regions
denote regions of no measurements.
to Journal of Geophysical Research, 2013). TES has much
coarser vertical resolution (~6–7 km versus ~2–4 km) but much
higher horizontal resolution (~10 km versus ~200 km) than the
other instruments in this study. Detailed information on
the individual instruments including their sampling patterns
and retrieval techniques can be found in the SPARC Data
Initiative report (section 2) and Hegglin et al. (manuscript in
preparation, 2013).
[9] Sampling patterns have been compiled for each instrument, defined as day, time, latitude, and longitude of measurement locations. For most instruments, a typical year of
actual sampling locations has been used in the analysis,
rather than, for instance, a time series of all possible measurements (which may differ for reasons such as data download
limitations). The particular years that were used to define
each instrument’s sampling pattern are included in Table 1.
Year-to-year variations in sampling patterns due to such factors as changing orbital states, changing instrument capabilities, or irregular data gaps—which may be significant for
a number of instruments—are not addressed by this study.
For Aura MLS, HIRDLS, MIPAS, and TES, month-tomonth variations in sampling are generally negligible, and
we have therefore used a typical month from their sampling
pattern and repeated this for all months of the year. For
SMR, sampling patterns are defined separately for O3 and
H2O, based on locations of retrieved profiles from the
501.8 GHz and 488.9 GHz measurement bands, respectively.
(In addition to the 488.9 GHz band H2O retrievals, which
extend from 20 to 70 km, SMR also produces climatologies
of H2O from ~16 to 20 km through measurements of the
544.6GHz band [Hegglin et al., 2013], however these
measurements are not considered here.) For SMILES, the
sampling patterns correspond to the samples over the full
lifetime of the mission, from October 2009 to April 2010.
[10] Monthly sample counts within the 5° bins of the
SPARC Data Initiative grid are shown for the instrumental
sampling patterns in Figure 1. The different sample patterns
of remote sounders of the stratosphere lead to substantial differences in the sample density patterns shown in Figure 1. Solar
occultation instruments typically have the sparsest sample
density, and therefore the smallest monthly sample counts, because their number of measurements is limited to a maximum
of two per orbit. The latitudinal coverage of solar occultation
instruments varies with time, leading to samples concentrated
within finite latitude ranges (usually one in the Northern
Hemisphere (NH) and one in the Southern Hemisphere (SH))
each month and also leaving unsampled latitudes each month.
Solar occultation instruments with high inclination orbits
(~57 to 74°, e.g., ACE-FTS, HALOE, and SAGE II) have
sampling which spans nearly the full globe over a year. Other
11,849
TOOHEY ET AL.: SAMPLING BIASES IN CLIMATOLOGIES
pressure [hPa]
O3 mean
O3 intra−monthly SD
0.1
0.1
1
1
1
10
10
10
100
100
−90
−45
0
45
90
100
−90
−45
0
45
90
−90
latitude [°]
H2O intra−monthly SD
latitude [°]
H2O mean
pressure [hPa]
O3 intra−monthly SD
0.1
0.1
0.1
1
1
1
10
10
10
100
100
100
−45
0
45
90
−90
−45
latitude [°]
0
5
0
45
90
−90
latitude [°]
10
0.2
ppmv
0.4
0.6
ppmv
0
45
90
latitude [°]
H2O intra−monthly SD
0.1
−90
−45
−45
0
45
90
latitude [°]
0.8
0
10
20
%
Figure 2. WACCM simulated O3 and H2O mean distribution and variability. (left) Annual mean O3 and
H2O, average of monthly standard deviations over 12 months in (middle) absolute and (right) percent.
solar occultation instruments (POAM II, POAM III, and SAGE
III) with Sun-synchronous orbits have sample ranges concentrated in the middle to high latitudes. Climatologies produced
for the stellar occultation instrument GOMOS use only night
measurements and therefore exclude measurements from the
polar summer. Instruments which measure scattered sunlight
(SCIAMACHY, OSIRIS) have denser sampling but are restricted to measuring within the sunlit portion of the atmosphere, leading to a smaller number of samples in the winter
hemisphere, which may be just the polar latitudes, or a larger
portion of the winter hemisphere depending on the pointing
of the instrument. Instruments which measure atmospheric
emission (Aura MLS, HIRDLS, MIPAS, SMILES, SMR,
TES, and UARS MLS) do not have such constraints related
to the radiation source, and thus typically have sampling coverage that is denser than solar occultation and limb scattering
instruments and relatively uniform with latitude and time. An
exception to the latter case is the sampling pattern of UARS
MLS, which produced measurements spanning 34° on one side
of the equator to 80° on the other side, with hemispheric coverage switching when the satellite performed a 180° yaw maneuver 10 times per year, at approximately 36 day intervals.
resolution at 0 UTC from 1 year of a transient simulation
under modern conditions.
[12] Annual zonal mean mixing ratios for O3 and H2O
are shown in Figure 2. Since sampling biases result from
nonuniform sampling of a varying field, we also show for reference a measure of “average variability” for the WACCM
fields, calculated by taking the standard deviation of the daily
fields for each month and averaging over the 12 calendar
months. The monthly standard deviations are calculated over
all model values for each latitude and pressure level, i.e., over
all times and longitudes, and as such represent the magnitude
of the variability due to temporal progression of the seasonal
cycle within any month and that due to dynamically induced
disturbances to zonal symmetry. Maximum variability of O3
is seen in the high latitudes, where the O3 seasonal cycle
is strongest, and where meridional gradients in the mean O3
field mean that dynamical variability results in chemical
variability. The variability of H2O mixing ratios is notably
weaker, a result of its weaker seasonal cycle and weaker
meridional gradients. Strongest variability of H2O is seen in
the SH lower stratosphere high latitudes and is a result of
the dehydration of the SH winter polar vortex.
2.2. Model Fields
[11] Chemical fields are taken from an integration of the
Whole Atmosphere Community Climate Model version 3
(WACCM3), a fully coupled chemistry-climate model,
spanning the range of altitude from the Earth’s surface to
the thermosphere [Garcia et al., 2007]. The particular version of the model used here (3.4.58) is essentially the same
as that used for the second Chemistry-Climate Model
Validation Activity [Morgenstern et al., 2010; SPARC
CCMVal, 2010]. The model’s horizontal resolution is 1.9°
by 2.5° (latitude by longitude). WACCM has been extensively evaluated as part of the SPARC CCMVal report
[2010]. WACCM has a good distribution and variability
of O3 and H2O in the stratosphere [SPARC CCMVal,
2010, chapter 9] and UTLS [Gettelman et al., 2010;
Hegglin et al., 2010]. We use here model output with daily
2.3. Sampling Bias Calculation
[13] Starting with full resolution model fields, the goal of
the exercise is to emulate as closely as possible the sampling
of each instrument and the climatology procedure used to produce the SPARC Data Initiative climatologies and compare
these climatologies to the “true” model climatology.
[14] First, the instrument sampling patterns for each month
of the year are used to subsample the model data. For each
sample, model fields from the corresponding Julian day are
linearly interpolated in space to the latitude and longitude
of the sample location. Once the model data have been
interpolated to each sample location, the subsampled fields
are processed in the same manner as the real measurements
in the production of climatologies, i.e., binned according
to the SPARC Data Initiative latitude grid, and the mean
calculated for each latitude bin and pressure surface. The
11,850
TOOHEY ET AL.: SAMPLING BIASES IN CLIMATOLOGIES
Figure 3. Latitude height sections of calculated RMS monthly percent sampling bias for O3, based on
sampling patterns of instruments as labeled in each panel. Gray regions denote regions of no measurements.
only exception is that in the case of MIPAS SPARC Data
Initiative climatologies, measured mixing ratios were interpolated to the central latitude of the bin, in order to avoid
sampling biases. This operation has not been accounted for
in this study; our analysis of the sampling error is based on
the original geolocations of the measurements. The true
model climatology, or population mean, is produced by first
calculating the mean of all model fields on each latitude circle
of the model’s latitude grid, then linearly interpolating these
mean values to the midpoint of each latitude bin. This interpolation is performed due to the fact that the two model latitudes (at 1.9° resolution) within each 5° latitude bin will not
be perfectly centered with respect to the bin midpoint, therefore simply averaging the model data within a latitude bin
could introduce a small sampling bias to the true model climatology. The difference between the instrument-samplingpattern-based subsampled field mean and the full-model-resolution field mean gives the sampling bias. For each month
and for each instrument, this bias is calculated for every latitude bin in which an instrument has measurements, and at all
pressure levels of the model fields. The vertical range of
presented results for each instrument is then “cropped”
based on the range of measurements in the corresponding
SPARC Data Initiative climatologies.
[15] This method produces an estimate of sampling bias
due to the horizontal sampling of the instruments, and no
effort is made here to understand differences between instrumental climatologies due to differences in the vertical resolution of the measurements. Furthermore, by using daily mean
model data, we cannot address possible biases in instrumental climatologies due to different sampling of a chemical
species’ diurnal cycle. As such, we apply our study here only
to chemical species with long stratospheric lifetimes.
[16] Ideally, in an exercise such as this, one would like the
resolution of the sampled model fields to be similar to the
horizontal resolution of the measurements they are meant to
emulate. This is because the variability of a sampled field
depends on the resolution of the measurement: measurements made at fine resolution will have larger variance
than those made at coarser resolution. While such issues
are important when comparing measured and modeled variability [e.g., Toohey et al, 2010], when examining average
values, the horizontal resolution should not have a large impact on the results, as long as sample sizes are large enough
that the mean is well estimated (i.e., the standard error of the
mean is small). Nevertheless, the resolution of the model
fields used here is roughly consistent with that of the limbsounding instruments—the horizontal resolution of limb
11,851
TOOHEY ET AL.: SAMPLING BIASES IN CLIMATOLOGIES
1 hPa anomalies
100
−90
−45
0
45
90
−10
80
2
−2
70
60
−90
−45
latitude
1
2
10
−2
100
−90
−45
0
45
90
−10
10
−2
100
−90
−45
0
45
90
−10
0
45
latitude
1 hPa anomalies
10 hPa anomalies
90
80
−10
2
−2
70
60
−90
−45
0
45
90 −90
−45
0
45
latitude
latitude
1 hPa anomalies
10 hPa anomalies
90
90
julian day
2
sampling bias [%]
pressure [hPa]
1
−45
10
OSIRIS
10
90 −90
latitude
latitude
0.1
45
90
julian day
10
sampling bias [%]
pressure [hPa]
MIPAS
0.1
0
anomalies [%]
−2
anomalies [%]
2
10
10
−10
10
80
2
−2
70
60
−90
−45
latitude
0
45
latitude
90 −90
−45
0
45
90
anomalies [%]
1
10 hPa anomalies
90
julian day
10
sampling bias [%]
pressure [hPa]
ACE−FTS
0.1
−10
latitude
Figure 4. (left column) March O3 percent sampling bias as function of latitude and pressure for ACEFTS, MIPAS, and OSIRIS sampling patterns. March WACCM zonal mean O3 intra-monthly percent
anomalies from the monthly mean are shown as a function of latitude and Julian day for the (middle
column) 1 hPa and (right column) 10 hPa surfaces, along with gray markers showing either the locations
of all samples (ACE-FTS) or the locations of latitude bins which contain measurements (MIPAS and
OSIRIS) based on each instrument’s sampling pattern.
sounding retrievals is typically on the order of a few hundred
kilometers [e.g., von Clarmann et al., 2009]. The model fields
used here have latitudinal resolution of about 200 km and
longitudinal resolution that ranges from about 250 km at the
equator to 200 km in the midlatitudes. At high latitudes, the
rough agreement between model and observation resolution
no longer holds, as the longitudinal resolution of the model
fields is finer than that of the observations; however, we find
(as shown in section 3) that estimated sampling biases are well
explained by mechanisms for which the horizontal resolution
of the model fields should not impact the results.
[17] Sampling biases calculated by the method described
above are the biases introduced to the monthly zonal mean
of model fields by the respective instrument sampling pattern. Whether the results represent reasonable estimates of
the true sampling bias for any instrument’s measurement
of the real atmosphere depends on how similar the model
fields are to reality. The model can be expected to reproduce in a fairly accurate way the seasonal cycle in chemical
trace gases, and short-term (subseasonal) variability can be
expected to be consistent with reality in a statistical sense.
However, it should be clear that any sampling bias estimate
resulting from short-term variability within this 1 year of
model data is simply one realization of potential sampling
bias. In this way, the sampling bias estimates should be considered example cases, and we focus on characterizing the
general features of sampling bias and its dependence on latitude and height for the given sampling patterns.
3.
Results
[18] Since sampling bias depends on the space-time gradients of the measured field, it can be different for different
trace gases. In the following, we explore sampling bias for
two trace gas species included in the SPARC Data Initiative
climatologies: O3 and H2O.
3.1. O3 Sampling Bias
3.1.1. Monthly Mean Sampling Bias
[19] Zonal mean sampling bias for O3 is shown for each instrument and each calendar month as a function of latitude and
height in the supporting information. To summarize the absolute magnitude and spatial structure of sampling bias, Figure 3
shows the root-mean-square (RMS) of the 12 monthly sampling bias estimates for each instrument.
[20] In general, at pressure levels above ~70 hPa, O3
sampling bias for all instruments is weak in the tropics
where intramonthly variability is weak (see Figure 2). In
the extratropics and polar latitudes, where variability is stronger, sampling bias becomes much larger. Sampling bias is
found to be weakest for the instruments with dense and uniform sampling density, Aura MLS, HIRDLS, MIPAS, and
TES. RMS bias for these instruments is less than 1% over
most of the stratosphere, with maximum values of 1–3%
occurring in isolated regions at the high latitudes, and
within the upper troposphere, where O3 mixing ratios are quite
small. SMR, SMILES, and SCIAMACHY have similarly
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TOOHEY ET AL.: SAMPLING BIASES IN CLIMATOLOGIES
ACE−FTS sampling bias
10
0
10
−5
100
−45
0
45
90
−90
ACE−FTS − MIPAS
−45
0
45
90
OSIRIS − MIPAS
10
pressure [hPa]
0.1
5
1
0
10
−5
100
−90
−45
0
45
−90
90
ACE−FTS − Aura MLS
−45
0
45
90
OSIRIS − Aura MLS
−10
10
0.1
pressure [hPa]
−10
5
1
0
10
−5
100
−90
−45
0
45
90
−90
latitude [°]
−45
0
45
difference [%]
−90
90
difference [%]
pressure [hPa]
5
1
sampling bias [%]
OSIRIS sampling bias
0.1
−10
latitude [°]
Figure 5. (top row) March O3 percent sampling bias for ACE-FTS and OSIRIS, as in Figure 3.
Differences between each instrument’s March O3 climatology and (middle row) MIPAS and (bottom
row) Aura MLS.
small (<1%) sampling bias through most of the tropical and
subtropical stratosphere, but with larger RMS sampling biases
in the middle to high latitudes. SMILES and SCIAMACHY
show RMS sampling bias of >1% poleward of 45° in the
NH and SH, respectively, while SMR and SCIAMACHY
sampling bias reaches >5% in regions of the high latitudes
of both hemispheres. RMS sampling bias of >2% covers most
of the middle to high latitudes for OSIRIS and UARS MLS,
and inspection of the monthly sampling bias plots reveals
that the results are variable in time, with large sampling bias
(>10%) in the middle to high latitudes for certain months of
the year. Finally, the occultation instruments ACE-FTS,
GOMOS, HALOE, POAM II, POAM III, SAGE II, and
SAGE III show strong sampling bias, with RMS values
greater than 5% over much of the high latitudes, and reaching
values of >10% in isolated locations. A number of these
instruments also show RMS sampling biases of 1–2% through
much of the tropical stratosphere. The large sampling biases at
high altitudes (above 0.4 hPa) calculated for many instruments
should be considered to be an artifact of the exercise, due to
the fact that O3 has an appreciable diurnal cycle at these
heights, and since the model fields are saved at 0 UTC, the
diurnal variability of O3 is expressed as a longitudinal structure in the O3 field.
[21] The largest sampling biases in Figure 3 can be understood to be a product of nonuniform sampling through
the days of a month, as can be seen when one examines
variations in O3 over a month, and the correlation of these
variations with instrument sampling patterns. Sampling
biases for the month of March are shown in Figure 4 for
ACE-FTS, MIPAS, and OSIRIS, as examples of sampling
bias estimates that span the range of results discussed above.
Sampling bias for this month is strong for ACE-FTS
(reaching values of >5%), weak for MIPAS, and strong for
OSIRIS in the SH. In Figure 4 (right column), the model
O3 field in March is shown in terms of percent anomalies
from the monthly zonal mean and plotted as a function of
latitude and Julian day for the 1 and 10 hPa pressure surfaces.
Included in these plots are gray markers indicating the latitude bins in each day which contain measurements based
on each instrument’s sampling pattern.
[22] The MIPAS sampling pattern contains measurements
in all latitude bins for all days: There is no variation in its sampling locations with time, and as a result, the sampling bias is
small. ACE-FTS, on the other hand, as a solar occultation instrument, samples each latitude band over only a few days of
the month. For example, in the month of March, SH midlatitudes (45°S) are sampled only at the very beginning of the
month, while SH high latitudes (80°S) are sampled only at
the very end of the month. At 1 hPa, O3 mixing ratios are increasing through the month over this latitude range; therefore,
the ACE-FTS sampling pattern leads to negative sampling
bias around 45°S, and slightly positive sampling bias
at the highest SH latitudes. The seasonal cycle of O3 is comparatively reversed at 10 hPa, leading to slightly positive bias
in the SH midlatitudes and negative bias in the SH high latitudes. In this way, it can be seen that the sampling biases of
ACE-FTS can be well explained by its sampling of the temporal variations in O3, which depend strongly on height and latitude. At 100 hPa, intramonthly O3 variations are relatively
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MIPAS
SCIAMACHY
10
pressure [hPa]
1
2
10
−2
100
latitude bias [°]
−90 −85 −80 −75 −70 −65 −60 −90 −85 −80 −75 −70 −65 −60 −90 −85 −80 −75 −70 −65 −60
2
2
2
1
1
1
0
0
0
−1
−1
−1
sampling bias [%]
Aura MLS
0.1
−10
−2
−2
−2
−90 −85 −80 −75 −70 −65 −60 −90 −85 −80 −75 −70 −65 −60 −90 −85 −80 −75 −70 −65 −60
latitude [°]
latitude [°]
latitude [°]
Figure 6. (top row) Sampling bias for September O3 in SH high latitudes for selected instruments with
(bottom row) differences between the latitude bin center and the mean sampled latitude.
noisy (not shown), and as a result, the sampling bias is dependent on the sampling of short-lived variability. We therefore
can expect that in regions where the sampling bias is due to
the nonuniform sampling of the slow seasonal variability
through a month, the sign and approximate magnitude of the
sampling bias calculated through our model exercise is a reasonably accurate estimate of the real sampling bias for each instrument. However, in regions where variability is dominated
by short-term (time scale of days) variations, limited sampling
of such a chemical field will lead to a random sampling error.
In this case, the sign and magnitude of the sample error calculated through our model exercise is only an example and
should be used only to identify regions where sampling error
may be important.
[23] The sampling pattern of OSIRIS in March is dense and
uniform in the NH, but it samples SH latitudes only within
the first half of the month. The OSIRIS sampling pattern,
and thus its sampling bias, is intermediate to the two extreme
cases explored above. As a result of the sampling pattern,
OSIRIS means in the SH are biased low at 1 hPa and high
at 10 hPa. This type of sampling bias occurs for OSIRIS in
months where its sampling pattern latitudinal range shifts from
one hemisphere to the other. Sampling biases for UARS MLS
come from a similar source due to its latitudinal coverage
shifting within months, leading to the mid to high latitudes
being sampled for only a portion of each month.
[24] The applicability of the sampling bias estimates to real
data is demonstrated through a brief case study. Assuming
small O3 sampling bias for MIPAS (as discussed above),
one would expect that the difference of another instrument’s
climatology with respect to that of MIPAS, e.g., ACE-FTS
minus MIPAS, should contain the effect of sampling bias
in the ACE-FTS climatology, in addition to measurement
errors. Figure 5 shows such differences for March climatologies
of ACE-FTS and OSIRIS, with differences calculated with
respect to both MIPAS and Aura MLS. Average values
are shown over 2 years: 2005–2006 for ACE-FTS comparisons and 2008–2009 for OSIRIS comparisons. Differences
between ACE-FTS and the dense sampling instruments
are dominated by positive values in the upper stratosphere
and mesosphere (3–0.1 hPa). This feature is independent
of latitude and is a common feature of comparisons between
ACE-FTS and other instruments [Dupuy et al., 2009]. Aside
from this primary feature, the signature of the estimated
sampling bias can be seen in the ACE-FTS comparisons:
For example, the main features of the sampling bias in the
SH, namely a negative bias at the highest SH latitudes between ~30 and 1 hPa and a negative bias in the midlatitude
upper stratosphere (60–45°S, 3–1 hPa) can be detected in
the ACE-FTS–MIPAS difference plot. In the NH, both
ACE-FTS–MIPAS and ACE-FTS–Aura MLS show negative differences in the high latitudes between 30 and 1
hPa, much of which is consistent with the sampling bias estimate. For OSIRIS, the sampling bias signature of a strong
negative bias in the SH upper stratosphere (3–0.8 hPa) is
clearly evident in both OSIRIS–MIPAS and OSIRIS–Aura
MLS difference plots. The predicted signature of positive
bias in the high-latitude SH lower stratosphere is also seen
in the OSIRIS–Aura MLS difference plots. The sampling bias
estimate plot for OSIRIS suggests however that the positive
difference between OSIRIS and both comparison instruments
in the NH lower stratosphere high latitudes is not a result of
sampling bias.
[25] Clearly, there are large differences between the climatologies shown in Figure 5 that are not explained by the sampling bias estimates, such as the positive difference between
ACE-FTS and other instruments in the upper stratosphere
and the negative bias of OSIRIS compared to MIPAS in
the upper stratosphere. Such biases are almost certainly due
to systematic biases in the measurements themselves. The
comparisons highlight, however, that in certain regions and
times, sampling biases make up a significant portion of the
difference between monthly mean climatologies.
[26] In addition to temporal considerations discussed
above, nonuniformity in latitude sampling can also lead to
sampling bias, which can be most notable at the northern
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50 hPa, 80−85° S
sampled O3 (ppmv)
3
2
ACE−FTS
Aura MLS
1
MIPAS
0
2
4
6
8
10
12
OSIRIS
POAM II
POAM III
sampling bias (%)
40
SCIAMACHY
20
SMR
TES
0
UARS MLS
−20
−40
2
4
6
8
10
12
month
Figure 7. (top) Sample mean model O3 and (bottom) relative sampling bias at 50 hPa in the 80–85°S latitude bin as a function of month of year, with sampling based on instrumental sampling patterns as defined
in legend.
and southern limits of instruments’ sampling patterns. In
these cases, instrumental sampling patterns typically do
not sample the full latitudinal extent of the latitude bin. If
the measured species has a significant gradient from one
side of the bin to the other, a sampling bias can occur.
This sampling bias likely occurs for all instruments and all
months to some degree but is most noticeable in cases
where other sampling biases are not present, e.g., at the extreme southern latitudes for the dense samplers Aura MLS,
HIRDLS, MIPAS and SMR.
[27] As an example, Figure 6 shows sampling biases from
selected instruments in the SH high latitudes for the month
of September, when Antarctic O3 depletion leads to a strong
gradient in O3 mixing ratio across the polar vortex. Figure 6
(bottom row) shows the bias in sampled latitude (mean sampled latitude minus latitude midpoint), which is seen to be
significant in the southernmost latitude bin of each instrument’s sampling range, due to the incomplete coverage of
this latitude band. Aura MLS, for example, samples only
the northern half of the 80–85°S bin, which leads to a positive sampling bias (of around 4%) in the Aura MLS climatology in this latitude bin at around 3 hPa. In comparison,
MIPAS samples the full 80–85°S bin, but only half of the
85–90°S bin. However, the latitudinal gradient in O3 is
weaker over this bin, so the MIPAS sampling bias at 3
hPa is smaller (~2%). All instruments display some degree
of latitudinal sampling bias at the edges of their sampling
domain; however, the bias in the measured field may be insignificant compared to other sources. For example, the bias
in sampled latitude at high latitudes for SCIAMACHY is
similar to the other instruments shown in Figure 6; however,
the sampling bias for O3 is dominated by temporal considerations since it measures only sunlit latitudes, in a way
that varies with time during this time of year in the southern
high latitudes. The bias seen for SCIAMACHY in the
mesosphere and in the UTLS at latitudes lower than 70°S
is most probably due to an exclusion of measurements over
the southern Atlantic (see below for details).
[28] The potential for sampling bias is greatest when temporal and spatial gradients of the measured field are largest.
The Antarctic O3 hole leads to extreme temporal change in
O3 mixing ratios and creates a strong gradient across the vortex edge in SH spring. The temporal evolution of sampling
bias in the 80–85°S latitude bin in the lower stratosphere
(50 hPa) is examined in Figure 7. Sampling bias is quite
small through most of the year but reaches values of ±30%
or more for some instruments in the SH spring months.
Most of the behavior shown in Figure 7 can be understood
in terms of previously discussed mechanisms. The low bias
of SCIAMACHY and OSIRIS in September is a result
of the fact that their measurements at high latitudes cover
only the latter half of the month, when O3 depletion has begun. A similar situation occurs for UARS MLS sampling in
October and December, leading to a low bias in October
and a high bias in December (for the sample year of UARS
MLS sampling used here). Slight biases in the 80–85°S
bin can be seen for Aura MLS and TES in November and
December due to latitudinal bias in this latitude bin, as
discussed above.
[29] Nonuniformity in sampled longitude can also lead to
sampling bias if the measured field is not zonally symmetric. This is, for example, the case for the SCIAMACHY
climatologies compiled for the SPARC Data Initiative. Due
to data quality issues, measurements over the South Atlantic
were not included in these climatologies, which results in a
systematically nonuniform sampling in longitude for latitudes
between 20°S and 70°S. The effect of this longitudinal sampling irregularity can be seen in the monthly mean sampling
bias plots for SCIAMACHY (see the supporting information),
which show systematically larger absolute magnitude sampling
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0
45
90 −90
−45
pressure [hPa]
0
45
90 −90
−45
MIPAS
0
45
90 −90
−45
OSIRIS
0
45
90
POAM II
0.1
1
10
100
−90
−45
0
45
90 −90
−45
POAM III
0
45
90 −90
−45
SAGE II
0
45
90 −90
SAGE III
−45
0
45
90
SCIAMACHY
0.1
1
10
100
−90
−45
0
45
90 −90
−45
SMILES
0
45
90 −90
−45
SMR
0
45
90 −90
TES
−45
0
45
90
1
10
100
−45
0
latitude [°]
45
90 −90
−45
0
45
90 −90
−45
latitude [°]
0
latitude [°]
1
0.5
0.2
0.1
0.05
0.02
0
1
0.5
0.2
0.1
0.05
0.02
0
UARS MLS
0.1
−90
1
0.5
0.2
0.1
0.05
0.02
0
sampling bias [σ]
−45
1
0.5
0.2
0.1
0.05
0.02
0
sampling bias [σ]
10
HIRDLS
pressure [hPa]
HALOE
1
−90
pressure [hPa]
GOMOS
sampling bias [σ]
Aura MLS
sampling bias [σ]
pressure [hPa]
ACE−FTS
0.1
45
90 −90
−45
0
45
90
latitude [°]
Figure 8. RMS O3 sampling biases for each instrument, as in Figure 3, but with monthly sampling biases
first normalized (by the standard deviation of O3), and therefore shown in units of σ rather than percent.
biases (with RMS values of >5%, see Figure 3) between 20
and 70°S latitude in the upper troposphere/lower stratosphere
(UTLS, approximately 300 to 70 hPa) and lower mesosphere
(approximately 1 to 0.1 hPa). The sampling biases at high altitudes should be considered to be an artifact, as discussed above.
However, the sampling biases shown for SCIAMACHY
climatologies in the UTLS are likely due to real longitudinal
dependence of UTLS O3 due to variations in tropospheric
chemistry and dynamics and should be considered when making use of the SCIAMACHY climatologies in the UTLS.
[30] It is clear from the discussion above that sampling
bias results from a combination of nonuniform sampling
and variability of the sampled field. With this in mind, it is
interesting to consider sampling biases normalized by the
variability of the chemical field. Figure 8 shows RMS O3
sampling biases, as in Figure 3, but normalized by the standard deviation of the O3 field. RMS normalized O3 sampling
bias shown in Figure 8 is more uniform with respect to
latitude and height compared to the percent values shown
in Figure 3. Maximum RMS normalized sampling biases,
as seen for the solar occultation instruments, are on the
order of approximately 0.5–1σ. For the dense sampling
instruments, RMS normalized sampling biases are typically
0–0.1σ. Normalizing by the standard deviation acts to better
isolate the impact of nonuniform instrumental sampling on
the sampling bias, making it independent of the magnitude
of the chemical field variability. In principle, the normalized
O3 sampling bias estimates could be used to calculate rough
sampling bias values for other long-lived trace gases which
show variability coherent with that of O3, if the variability
of the chemical field is known.
3.1.2. Annual Mean Sampling Bias
[31] To assess how sampling bias can affect annual mean
climatologies, we produce annual mean sampling bias estimates for each instrument by calculating annual averages of
the sampled monthly mean fields for each instrument, then
calculating the percent difference of this quantity compared
to the model annual mean. The annual mean bias therefore includes not only the sampling biases present in the monthly
mean biases discussed above but also any bias due to an instrument’s incomplete sampling over the year for any latitude
bin. Annual sampling biases for O3 are shown for each instrument in Figure 9.
[32] The instruments with uniform sampling throughout the
year (Aura MLS, HIRDLS, MIPAS, SMR, and TES) show
very weak annual mean sampling biases of only a few percent.
In contrast, the annual mean sampling biases for the other
instruments, all of which have latitudinal sampling which
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2
−2
10
100
0
45
90 −90
−45
0
pressure [hPa]
45
90 −90
−45
MIPAS
0
45
90 −90
−45
OSIRIS
0
45
−10
90
POAM II
10
0.1
1
2
−2
10
100
−90
−45
0
45
90 −90
−45
0
POAM III
45
90 −90
−45
SAGE II
0
45
90 −90
SAGE III
−45
0
45
−10
90
SCIAMACHY
10
0.1
1
2
−2
10
100
−90
−45
0
45
90 −90
−45
0
SMILES
45
90 −90
−45
0
SMR
45
90 −90
TES
−45
0
45
−10
90
UARS MLS
10
0.1
1
2
−2
10
100
−90
−45
0
45
90 −90
latitude [°]
−45
0
45
90 −90
−45
latitude [°]
0
sampling bias [%]
−45
sampling bias [%]
10
HIRDLS
pressure [hPa]
HALOE
1
−90
pressure [hPa]
GOMOS
sampling bias [%]
Aura MLS
45
90 −90
latitude [°]
−45
0
45
−10
90
sampling bias [%]
pressure [hPa]
ACE−FTS
0.1
latitude [°]
Figure 9. Latitude height sections of calculated annual mean percent sampling bias for O3, based on sampling patterns of instruments as labeled in each panel. Gray regions denote regions of no measurements.
varies throughout the year, are considerable, often exceeding
10%, and reaching values of >20% in some cases. The annual mean sampling biases can be qualitatively explained
by the seasonality of sampling. For example, the SMILES
ACE−FTS
sampling pattern covers only approximately half the year,
during NH winter and spring. Clearly, some sampling bias
is to be expected when calculating an annual mean with a half
year of SMILES data, and while this example is perhaps not
Aura MLS
HIRDLS
MIPAS
100
1
−1
200
300
−90
−45
0
45
90 −90
OSIRIS
−45
0
45
90 −90
−45
SCIAMACHY
0
45
90 −90
−45
0
45
90
−5
latitude [°]
TES
70
pressure [hPa]
sampling bias [%]
5
5
100
1
−1
200
300
−90
−45
0
latitude [°]
45
90 −90
−45
0
45
90 −90
latitude [°]
−45
0
45
90
latitude [°]
Figure 10. Annual mean O3 sampling biases in the UTLS for instruments with applicable vertical coverage.
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sampling bias [%]
pressure [hPa]
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TOOHEY ET AL.: SAMPLING BIASES IN CLIMATOLOGIES
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10
2
1
100
−45
0
45
90 −90
−45
0
45
90 −90
−45
SAGE II
0
45
90 −90
SAGE III
−45
0
45
90
0
SCIAMACHY
0.1
20
10
1
5
10
2
1
100
−90
−45
0
45
90 −90
SMR
−45
0
45
90 −90
−45
0
latitude [°]
UARS MLS
45
90 −90
−45
0
45
90
0
latitude [°]
0.1
20
10
1
5
10
2
1
100
−90
−45
0
latitude [°]
45
90 −90
−45
0
45
sampling bias [%]
10
1
POAM III
pressure [hPa]
MIPAS
20
−90
pressure [hPa]
HALOE
sampling bias [%]
Aura MLS
0
90
sampling bias [%]
pressure [hPa]
ACE−FTS
0.1
latitude [°]
Figure 11. Latitude height sections of calculated RMS monthly percent sampling error for H2O, based on
sampling patterns of instruments as labeled in each panel. Gray regions denote regions of no measurements.
realistic, it helps to illustrate the mechanism behind the sampling biases of other instruments with less dramatic sampling
nonuniformity throughout the year. The annual mean sampling
bias for the SMILES sampling pattern in each hemisphere is
characterized by a “tripole” pattern, with alternating sign with
height, and is opposite in sign in each hemisphere. OSIRIS
does not sample the high-latitude winters (Figure 1), and as
a result, the annual mean sampling bias pattern shows the
characteristic tripole pattern in the high latitudes, which is similar in morphology with the SMILES sampling bias in the
“summer” SH. HALOE, SAGE II, and SCIAMACHY show
similar biases toward summer sampling (see again Figure 1),
leading to similar sampling bias morphology for these instruments. GOMOS sampling is biased toward winter in the high
latitudes; as a result, its annual mean sampling pattern has
a similar structure to that of OSIRIS, HALOE, SAGE II,
and SCIAMACHY but with opposite sign. The more complicated annual mean sampling bias morphologies of ACE-FTS,
POAM II, POAM III, and SAGE III result from the more complicated patterns of their sampling. For example, ACE-FTS
samples the highest latitudes during autumn and early spring,
with a lack of samples at these latitudes through the summer
months. As a result, the annual mean sampling for the highest
latitudes resembles that of GOMOS, while in the midlatitudes,
ACE-FTS sampling covers most of the summer months but
less of the winter, leading to a sign change in the sampling bias
for any pressure level moving equatorward. A similar mechanism explains the complicated structures of the POAM II,
POAM III, and SAGE III annual mean sampling biases.
[33] Figure 10 details the calculated annual mean sampling
biases within the UTLS for instruments with applicable
measurement ranges. A common feature of many of the
instrumental sampling biases is positive biases around 30°N
and S between 200 and 100 hPa. In these regions, the tropopause slopes downward with latitude, creating a strong horizontal O3 gradient on pressure surfaces. Instrumental
sampling densities tend to increase modestly with latitude.
As a result, within the latitude band that straddles the tropopause for a given pressure surface, instruments tend to sample the poleward side of the latitude band slightly more
often than the equatorward side, leading to positive bias in
the average O3 mixing ratio. This feature is apparent to different degrees in the UTLS sampling bias estimates for Aura
MLS, HIRDLS, MIPAS, and TES. The sampling biases for
ACE-FTS and OSIRIS are dominated by nonuniform month
of year sampling issues as discussed above, and for
SCIAMACHY, the nonuniformity of longitudinal sampling
is seen to have an influence between 20 and 70°S, seemingly
amplifying the magnitude of the tropopause-related bias
at 30°S.
3.2. H2O Sampling Bias
3.2.1. Monthly Mean Sampling Bias
[34] Monthly mean sampling bias results for H2O are
shown in the supporting information plots. To summarize
the absolute magnitude and spatial structure of H2O sampling
bias for each instrument, Figure 11 shows the RMS of the
12 monthly sampling bias estimates for each instrument.
[35] Sampling bias for H2O is generally smaller than for
O3. For example, solar occultation instruments which had
sampling biases of greater than 5% over large portions of
the high latitudes (poleward of ±50°) for O3 have H2O sampling biases of 2% or less over most of the NH. This is related
to the weaker temporal and spatial variability of stratospheric
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45
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−2
250
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2
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100
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45
latitude [°]
1 hPa anomalies
30 hPa anomalies
90
−10
10
−2
250
−45
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45
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−45
0
45
latitude [°]
latitude [°]
1 hPa anomalies
30 hPa anomalies
90
−10
10
270
julian day
2
−2
10
0
2
−90
sampling bias [%]
pressure [hPa]
1
−45
260
SCIAMACHY
10
90 −90
latitude [°]
latitude [°]
0.1
45
270
julian day
pressure [hPa]
ACE−FTS
0.1
sampling bias [%]
latitude [°]
0
anomalies [%]
−2
10
270
anomalies [%]
2
10
30 hPa anomalies
2
−2
260
250
−90
−45
latitude [°]
0
latitude [°]
45
90 −90
−45
0
45
90
anomalies [%]
1
1 hPa anomalies
julian day
10
sampling bias [%]
pressure [hPa]
Aura MLS
0.1
−10
latitude [°]
Figure 12. (left column) September H2O percent sampling bias as function of latitude and pressure for
Aura MLS, ACE-FTS, and SCIAMACHY sampling patterns. September WACCM zonal mean intramonthly percent anomalies from the monthly mean are shown as a function of latitude and Julian day for
the (middle column) 1 hPa and (right column) 30 hPa surfaces, along with gray markers showing either
the locations of all samples (ACE-FTS) or the locations of latitude bins which contain measurements
(Aura MLS and SCIAMACHY) based on each instrument’s sampling pattern.
H2O compared to that of O3 (see Figure 2), and in fact RMS
normalized H2O sampling biases (normalized by the H2O
standard deviation, not shown) are quite similar to those of
O3 shown in Figure 8. One location of strong H2O sampling
bias is the high SH latitudes, where dehydration of the SH
winter vortex leads to strong gradients in space across the
vortex edge and temporal gradients during the period of dehydration and recovery. Most solar occultation instruments
(all but SAGE III, which does not measure in the high SH
latitudes) show signs of the impact of vortex dehydration in
their H2O sampling biases. Larger biases are seen for the instruments with irregular temporal sampling, e.g., ACE-FTS,
HALOE, POAM II, POAM III, SAGE II, SCIAMACHY,
SMR, and UARS MLS.
[36] Figure 12 illustrates the impact of irregular temporal
sampling in the month of September, when SH vortex H2O
values increase over the month, with short-term variability
superimposed on the steady recovery in the lower stratosphere.
Aura MLS sampling is uniform, and as a result, the calculated
sampling bias is small (<2%, except for the highest SH latitudes, as discussed below). ACE-FTS samples the highest
SH latitudes only at the beginning of the month, leading to a
low bias in its monthly mean estimate, which is strongest in
the lowest stratosphere (>10%) but also present in the upper
stratosphere (>4%). In contrast, SCIAMACHY sampling follows the return of sunlight to the highest latitudes, so its
sampling of the highest SH latitudes occurs in the latter half
of the month, leading to a positive bias (reaching values
>10%) compared to the true monthly mean.
[37] Aura MLS and MIPAS, which have temporally
invariant sampling patterns, also show sampling bias in
the high SH latitudes. As was shown for O3, the strong gradient in H2O across the vortex edge and the nonuniform
sampling of the southernmost latitude bin lead to bias at that
latitude. Figure 13 shows SH high-latitude H2O sampling
biases for Aura MLS, MIPAS, and SCIAMACHY in
September and the bias in sampled latitude. The incomplete
sampling of the latitude band can lead to biases of more than
10%, due to the strong gradient in H2O and its very low
mixing ratios.
3.2.2. Annual Mean Sampling Bias
[38] Annual mean sampling biases are shown in Figure 14
for H2O. As was the case for O3, the annual mean sampling
bias for Aura MLS and MIPAS—instruments with relatively
uniform seasonal sampling—is small throughout all of the
stratosphere, while sizeable sampling biases are computed
for instruments with seasonally varying coverage. Many instruments (HALOE, POAM II, SAGE II, SCIAMACHY,
and SMR) show a low bias in the SH high-latitude lower
stratosphere (reaching values of at least 8%), resulting
from the fact that these instruments sample the H2O mixing
ratio minimum in SH spring following the dehydration of
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TOOHEY ET AL.: SAMPLING BIASES IN CLIMATOLOGIES
MIPAS
SCIAMACHY
10
1
2
10
−2
100
latitude bias [°]
−90 −85 −80 −75 −70 −65 −60 −90 −85 −80 −75 −70 −65 −60 −90 −85 −80 −75 −70 −65 −60
2
2
2
1
1
1
0
0
0
−1
−1
−1
−10
sampling bias [%]
pressure [hPa]
Aura MLS
0.1
−2
−2
−2
−90 −85 −80 −75 −70 −65 −60 −90 −85 −80 −75 −70 −65 −60 −90 −85 −80 −75 −70 −65 −60
latitude [°]
latitude [°]
latitude [°]
Figure 13. (top row) Sampling bias for September H2O in SH high latitudes for selected instruments with
(bottom row) differences between the latitude bin center and the mean sampled latitude.
[39] Monthly zonal mean climatologies produced through
the method of binning and averaging measurements into
months and 5° latitude bands may contain nonnegligible
biases of >10% in some cases due to the nonuniform
MIPAS
10
1
2
−2
10
100
−45
0
45
90 −90
−45
0
45
90 −90
−45
0
45
90 −90
SAGE III
SAGE II
−45
0
45
90
−10
SCIAMACHY
10
0.1
1
2
−2
10
100
−90
−45
0
45
90 −90
SMR
−45
0
45
90 −90
−45
0
latitude [°]
UARS MLS
45
90 −90
−45
0
45
90
−10
latitude [°]
10
0.1
1
2
−2
10
100
−90
−45
0
latitude [°]
45
90 −90
−45
0
45
90
latitude [°]
Figure 14. Latitude height sections of calculated annual mean percent sampling bias for H2O, based on
sampling patterns of instruments as labeled in each panel. Gray regions denote regions of no measurements.
11,860
sampling bias [%]
HALOE
Aura MLS
POAM III
pressure [hPa]
Conclusions
0.1
−90
pressure [hPa]
4.
sampling bias [%]
pressure [hPa]
ACE−FTS
density and uniform sampling of instruments like Aura
MLS and MIPAS.
−10
sampling bias [%]
the polar vortex but tend to undersample the maximum in
H2O mixing ratios during SH fall and winter. ACE-FTS,
on the other hand, samples the highest SH latitudes only
during March and April, leading to a >10% positive sampling bias there. For occultation instruments whose vertical
range extends into the UTLS, sampling bias is large in the
UTLS, with values >10%. It is clear that due to the significant
variability of H2O in the UTLS region, an accurate estimation of the annual mean H2O mixing ratio requires the high
TOOHEY ET AL.: SAMPLING BIASES IN CLIMATOLOGIES
temporal and spatial sampling of the atmosphere performed
by the instruments. We have examined sampling biases
produced by the sampling patterns of 16 instruments participating in the SPARC Data Initiative when applied to
coupled chemistry-climate model output of O3 and H2O
fields. Keeping in mind that our results are based on a single
year of simulated fields from a single model, and the sampling patterns are based on single years of satellite measurements, a number of general statements regarding the impact
of sampling bias on trace gas climatologies can be made.
Specifically, we find that:
[40] 1. Climatologies built from measurements from instruments with regular and uniform sampling patterns have
generally small sampling bias. Sampling bias may still exist,
however, when the sampled latitudes within latitude bins are
not uniformly distributed. For example, incomplete coverage
of the northernmost and southernmost latitude bins can lead
to sampling bias in those bins. This type of sampling bias appears most significantly in the high southern latitudes during
SH winter, when the Antarctic vortex produces particularly
strong latitudinal gradients.
[41] 2. Climatologies built from measurements from instruments whose latitudinal coverage varies with time can
have strong sampling biases for certain months and locations.
Sampling biases for O3 were found in some instances to be as
large as 10–40%. This is primarily due to nonuniformity in
day-of-month sampling and occurs whenever an instrument
provides measurements over only a portion of the month.
In cases for which the atmospheric variability is dominated
by the seasonal cycle, this type of sampling error could in
theory be reasonably well quantified or even corrected, however, when variability is dominated by short-term random
fluctuations only the absolute magnitude of the sampling bias
can be estimated from model studies. This type of sampling
bias is most relevant for solar occultation instruments but
is also important for any instrument whose sampling of certain latitudes is not uniform in time.
[42] 3. Sampling bias is a function not only of the sampling
pattern but also the time-space variability of the field being
averaged. Throughout most of the stratosphere, sampling
bias is much more important for O3 than for H2O, since the
variability of O3 is stronger. A normalized sampling bias,
shown in Figure 8, isolates the impact of an instrument’s
nonuniform sampling and can in principle be used to produce
rough estimates of potential sampling bias for other longlived trace gases if the variability of the trace gas is known.
[43] 4. In the UTLS region, space-time gradients in O3 and
H2O (and in fact most trace gas species) are strong, and sampling bias is important. Instruments with uniform temporal
sampling have monthly mean sampling biases of a few percent in the UTLS, while instruments with nonuniform temporal sampling have sampling biases of up to 10%. Due to the
random nature of sampling bias in the UTLS, sampling
biases are somewhat reduced in annual means. However,
even for instruments with dense and uniform sampling, the
strong horizontal gradients in chemical mixing ratios across
the subtropical tropopause can lead to annual mean sampling
biases of 1–2%.
[44] Users of monthly zonal mean climatologies of trace
gases, including those of the SPARC Data Initiative, are
encouraged to keep these results in mind when using such data
products for chemistry-climate model validation, assessments
of observed variability, or other applications. It should be understood that in some cases, the inter-instrument spread of the climatologies is larger than the uncertainty in the true fields due to
measurement errors. In such cases, the climatologies of instruments with highest sampling density should be considered more
representative estimates of the truth, in the sense that differences
between the climatologies and the true atmospheric mean state
should be dominated by measurement error rather than sampling biases. It should also be noted that no instrumental climatology produced by binning of measurements into latitude bins
is completely free of the influence of sampling bias, as even
modest irregularities in sampling over latitude bins can lead to
sampling biases of a few percent in regions of strong meridional
gradients, such as across the polar vortices and the tropopause.
[45] Acknowledgments. The SPARC Data Initiative thanks the
International Space Science Institute in Bern (ISSI) who supported the activity
through their ISSI International Team activity program, and the World
Climate Research Programme and the Toronto SPARC office for generous
travel funds. The work by Matthew Toohey is supported by the BMBF
MIKLIP project ALARM through the grant 01LP1130B. Michaela Hegglin
thanks the Canadian Space Agency (CSA) and the European Space Agency
for supporting her work for the SPARC Data Initiative. The work from
Susann Tegtmeier was funded from the WGL project TransBrom and the EU
project SHIVA (FP7-ENV-2007-1-226224). The work from Hampton
University was partially funded under the National Oceanic and Atmospheric
Administration’s Educational Partnership Program Cooperative Remote
Sensing Science and Technology Center (NOAA EPP CREST). Work at the
Jet Propulsion Laboratory, California Institute of Technology, was performed
under contract with the National Aeronautics and Space Administration. ACE
is a Canadian-led mission mainly supported by the CSA. Development of
the ACE-FTS climatologies was supported by grants from the Canadian
Foundation for Climate and Atmospheric Sciences and the CSA. Odin is
a Swedish-led satellite project funded jointly by the Swedish National Space
Board (SNSB), the CSA, the National Technology Agency of Finland
(Tekes), the Centre National d’Etudes Spatiales (CNES) in France, and the
Third Party Mission program of ESA. The work of E. Kyrölä was supported
by the Academy of Finland through the project MIDAT (134325). Work on
HIRDLS was supported by NASA’s EOS Program in the U.S. and in the UK
by NERC. IAA was supported by the Spanish MINECO under grant
AYA2011-23552 and EC FEDER funds. The work of the University of
Bremen team on SCIAMACHY climatologies was funded in part by the
German Aerospace Agency (DLR) within the project SADOS (50EE1105),
by the DFG Research Unit FOR 1095 “Stratospheric Change and its role
for Climate Prediction (SHARP)” (project GZ WE 3647/3-1), and by the
State and University of Bremen. WACCM simulations were performed in
the Centro de Supercomputacion de Galicia under a Reto2009 Project, and
the authors thank Rolando García, who developed the WACCM model version
used here, and Andrew Gettelman for guidance with the model. Finally, the
authors thank Ted Shepherd, Peter Braesicke, and Karen Rosenlof for helpful
feedback on early results from this work, and two anonymous reviewers who
provided valuable comments on the submitted manuscript.
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